Noise, resolution, and sensitivity considerations in the design of a single-slice emission-transmission computed tomographic system

A prototype Emission-Transmission Computed Tomography (ETCT) system is being developed that will acquire single-slice x-ray transmission CT images simultaneously with single photon emission computed tomography (SPECT) images. This system will permit the correlation of anatomical information from x-ray CT with functional information from SPECT images. The patient-specific attenuation map derived from the x-ray CT images can be used to perform attenuation correction of the SPECT images, so that accurate quantitative information can be obtained. The fan-beam scanning geometry and the use of a segmented HPGe detector array impose special constraints on the design of the collimator for the system. Based on a signal detection model, an efficiency-resolution figure of merit (ERFM) as a function of the collimator geometric efficiency, system resolution width, and object diameter is defined. The ERFM is proportional to the square of the detection signal-to-noise ratio. The collimator design parameters can then be optimized by optimizing the ERFM for an anticipated object diameter. The collimator point-spread function, geometric efficiency, and resolution are calculated. The collimator optimized for the detection of a 1-cm object will have a single-slice point source efficiency of 1.2 X 10(-4), and a FWHM of 6.5 mm at the center of the reconstruction circle, at 12 cm from the collimator face. The minimum object contrast which will give a detection SNR of 5 is 74%, for a total accumulated count per slice of 2 X 10(6).     

MR-based keyhole SPECT for small animal imaging

The rationale for multi-modality imaging is to integrate the strengths of different imaging technologies while reducing the shortcomings of an individual modality. The work presented here proposes a limited-field-of-view (LFOV) SPECT reconstruction technique that can be implemented on a multi-modality MR/SPECT system that can be used to obtain simultaneous MRI and SPECT images for small animal imaging. The reason for using a combined MR/SPECT system in this work is to eliminate any possible misregistration between the two sets of images when MR images are used as a priori information for SPECT. In nuclear imaging the target area is usually smaller than the entire object; thus, focusing the detector on the LFOV results in various advantages including the use of a smaller nuclear detector (less cost), smaller reconstruction region (faster reconstruction) and higher spatial resolution when used in conjunction with pinhole collimators with magnification. The MR/SPECT system can be used to choose a region of interest (ROI) for SPECT. A priori information obtained by the full field-of-view (FOV) MRI combined with the preliminary SPECT image can be used to reduce the dimensions of the SPECT reconstruction by limiting the computation to the smaller FOV while reducing artifacts resulting from the truncated data. Since the technique is based on SPECT imaging within the LFOV it will be called the keyhole SPECT (K-SPECT) method. At first MRI images of the entire object using a larger FOV are obtained to determine the location of the ROI covering the target organ. Once the ROI is determined, the animal is moved inside the radiofrequency (rf) coil to bring the target area inside the LFOV and then simultaneous MRI and SPECT are performed. The spatial resolution of the SPECT image is improved by employing a pinhole collimator with magnification >1 by having carefully calculated acceptance angles for each pinhole to avoid multiplexing. In our design all the pinholes are focused to the center of the LFOV. K-SPECT reconstruction is accomplished by generating an adaptive weighting matrix using a priori information obtained by simultaneously acquired MR images and the radioactivity distribution obtained from the ROI region of the SPECT image that is reconstructed without any a priori input. Preliminary results using simulations with numerical phantoms show that the image resolution of the SPECT image within the LFOV is improved while minimizing artifacts arising from parts of the object outside the LFOV due to the chosen magnification and the new reconstruction technique. The root-mean-square-error (RMSE) in the out-of-field artifacts was reduced by 60% for spherical phantoms using the K-SPECT reconstruction technique and by 48.5-52.6% for the heart in the case with the MOBY phantom. The K-SPECT reconstruction technique significantly improved the spatial resolution and quantification while reducing artifacts from the contributions outside the LFOV as well as reducing the dimension of the reconstruction matrix.     

The effects of object activity distribution on multiplexing multi-pinhole SPECT

We aim to study the effects of activity distribution for multiplexing multi-pinhole (MPH) SPECT. Three digital phantoms, including a hot rod, a cold rod and a cold sphere phantom, were used. Different degrees of multiplexing were obtained by (i) adjusting the MPH pattern for the same 4-pinhole collimator (scheme 1) and (ii) increasing the number of pinholes (scheme 2). Noise-free and noisy projections were generated using a 3D analytical MPH projector based on the same acquisition time. Projections were reconstructed using OS-EM without resolution recovery. Normalized mean-square-error (NMSE), noise, image profiles and signal-to-background ratios (SBR) were assessed. For the hot rod phantom, the NMSE-noise trade-offs slightly improves for multiplexing designs in scheme 2. Substantial artifacts were observed and the NMSE-noise trade-offs slightly worsened for multiplexing designs for the cold phantoms. Resolutions slightly degraded for higher degrees of multiplexing (～39-65%) for the cold rod phantom. For the cold sphere phantom, image profiles showed non-multiplexing designs better emulated the phantom, while ～20% multiplexing performs similarly as compared to non-multiplexing in SBR. Our results indicate that multiplexing can help for sparse objects but leads to a significant image degradation in non-sparse distributions. Since many tracers are not highly specific, and the gain of detection efficiency by allowing multiplexing is fairly offset by image degradations, multiplexing needs to be kept to a minimum for optimum MPH collimator designs.     

An investigation of inconsistent projections and artefacts in multi-pinhole SPECT with axially aligned pinholes

Multiple pinholes are advantageous for maximizing the use of the available field of view (FOV) of compact small animal single photon emission computed tomography (SPECT) detectors. However, when the pinholes are aligned axially to optimize imaging of extended objects, such as rodents, multiplexing of the pinhole projections can give rise to inconsistent data which leads to 'ghost point' artefacts in the reconstructed volume. A novel four pinhole collimator with a baffle was designed and implemented to eliminate these inconsistent projections. Simulation and physical phantom studies were performed to investigate artefacts from axially aligned pinholes and the efficacy of the baffle in removing inconsistent data and, thus, reducing reconstruction artefacts. SPECT was performed using a Defrise phantom to investigate the impact of collimator design on FOV utilization and axial blurring effects. Multiple pinhole SPECT acquired with a baffle had fewer artefacts and improved quantitative accuracy when compared to SPECT acquired without a baffle. The use of four pinholes positioned in a square maximized the available FOV, increased acquisition sensitivity and reduced axial blurring effects. These findings support the use of a baffle to eliminate inconsistent projection data arising from axially aligned pinholes and improve small animal SPECT reconstructions.     

Study of noise propagation and the effects of insufficient numbers of projection angles and detector samplings for iterative reconstruction using planar-integral data

A rotating slat collimator can be used to acquire planar-integral data. It achieves higher geometric efficiency than a parallel-hole collimator by accepting more photons, but the planar-integral data contain less tomographic information that may result in larger noise amplification in the reconstruction. Lodge evaluated the rotating slat system and the parallel-hole system based on noise behavior for an FBP reconstruction. Here, we evaluate the noise propagation properties of the two collimation systems for iterative reconstruction. We extend Huesman's noise propagation analysis of the line-integral system to the planar-integral case, and show that approximately 2.0(D/dp) SPECT angles, 2.5(D/dp) self-spinning angles at each detector position, and a 0.5dp detector sampling interval are required in order for the planar-integral data to be efficiently utilized. Here, D is the diameter of the object and dp is the linear dimension of the voxels that subdivide the object. The noise propagation behaviors of the two systems are then compared based on a least-square reconstruction using the ratio of the SNR in the image reconstructed using a planar-integral system to that reconstructed using a line-integral system. The ratio is found to be proportional to the square root of F/D, where F is a geometric efficiency factor. This result has been verified by computer simulations. It confirms that for an iterative reconstruction, the noise tradeoff of the two systems is not only dependent on the increase of the geometric efficiency afforded by the planar projection method, but also dependent on the size of the object. The planar-integral system works better for small objects, while the line-integral system performs better for large ones. This result is consistent with Lodge's results based on the FBP method.     

A three-dimensional ray-driven attenuation, scatter and geometric response correction technique for SPECT in inhomogeneous media

The qualitative and quantitative accuracy of SPECT images is degraded by physical factors of attenuation, Compton scatter and spatially varying collimator geometric response. This paper presents a 3D ray-tracing technique for modelling attenuation, scatter and geometric response for SPECT imaging in an inhomogeneous attenuating medium. The model is incorporated into a three-dimensional projector-backprojector and used with the maximum-likelihood expectation-maximization algorithm for reconstruction of parallel-beam data. A transmission map is used to define the inhomogeneous attenuating and scattering object being imaged. The attenuation map defines the probability of photon attenuation between the source and the scattering site, the scattering angle at the scattering site and the probability of attenuation of the scattered photon between the scattering site and the detector. The probability of a photon being scattered through a given angle and being detected in the emission energy window is approximated using a Gaussian function. The parameters of this Gaussian function are determined using physical measurements of parallel-beam scatter line spread functions from a non-uniformly attenuating phantom. The 3D ray-tracing scatter projector-backprojector produces the scatter and primary components. Then, a 3D ray-tracing projector-backprojector is used to model the geometric response of the collimator. From Monte Carlo and physical phantom experiments, it is shown that the best results are obtained by simultaneously correcting attenuation, scatter and geometric response, compared with results obtained with only one or two of the three corrections. It is also shown that a 3D scatter model is more accurate than a 2D model. A transmission map is useful for obtaining measurements of attenuation and scatter in SPECT data, which can be used together with a model of the geometric response of the collimator to obtain corrected images with quantitative and diagnostically accurate information.     

Lutetium oxyorthosilicate (LSO) intrinsic activity correction and minimal detectable target activity study for SPECT imaging with a LSO-based animal PET scanner

This work is part of a feasibility study to develop SPECT imaging capability on a lutetium oxyorthosilicate (LSO) based animal PET system. The SPECT acquisition was enabled by inserting a collimator assembly inside the detector ring and acquiring data in singles mode. The same LSO detectors were used for both PET and SPECT imaging. The intrinsic radioactivity of (176)Lu in the LSO crystals, however, contaminates the SPECT data, and can generate image artifacts and introduce quantification error. The objectives of this study were to evaluate the effectiveness of a LSO background subtraction method, and to estimate the minimal detectable target activity (MDTA) of image object for SPECT imaging. For LSO background correction, the LSO contribution in an image study was estimated based on a pre-measured long LSO background scan and subtracted prior to the image reconstruction. The MDTA was estimated in two ways. The empirical MDTA (eMDTA) was estimated from screening the tomographic images at different activity levels. The calculated MDTA (cMDTA) was estimated from using a formula based on applying a modified Currie equation on an average projection dataset. Two simulated and two experimental phantoms with different object activity distributions and levels were used in this study. The results showed that LSO background adds concentric ring artifacts to the reconstructed image, and the simple subtraction method can effectively remove these artifacts-the effect of the correction was more visible when the object activity level was near or above the eMDTA. For the four phantoms studied, the cMDTA was consistently about five times of the corresponding eMDTA. In summary, we implemented a simple LSO background subtraction method and demonstrated its effectiveness. The projection-based calculation formula yielded MDTA results that closely correlate with that obtained empirically and may have predicative value for imaging applications.     

Integration of SimSET photon history generator in GATE for efficient Monte Carlo simulations of pinhole SPECT

The authors developed and validated an efficient Monte Carlo simulation (MCS) workflow to facilitate small animal pinhole SPECT imaging research. This workflow seamlessly integrates two existing MCS tools: simulation system for emission tomography (SimSET) and GEANT4 application for emission tomography (GATE). Specifically, we retained the strength of GATE in describing complex collimator/detector configurations to meet the anticipated needs for studying advanced pinhole collimation (e.g., multipinhole) geometry, while inserting the fast SimSET photon history generator (PHG) to circumvent the relatively slow GEANT4 MCS code used by GATE in simulating photon interactions inside voxelized phantoms. For validation, data generated from this new SimSET-GATE workflow were compared with those from GATE-only simulations as well as experimental measurements obtained using a commercial small animal pinhole SPECT system. Our results showed excellent agreement (e.g., in system point response functions and energy spectra) between SimSET-GATE and GATE-only simulations, and, more importantly, a significant computational speedup (up to approximately 10-fold) provided by the new workflow. Satisfactory agreement between MCS results and experimental data were also observed. In conclusion, the authors have successfully integrated SimSET photon history generator in GATE for fast and realistic pinhole SPECT simulations, which can facilitate research in, for example, the development and application of quantitative pinhole and multipinhole SPECT for small animal imaging. This integrated simulation tool can also be adapted for studying other preclinical and clinical SPECT techniques.     

Joint optimization of collimator and reconstruction parameters in SPECT imaging for lesion quantification

Obtaining the best possible task performance using reconstructed SPECT images requires optimization of both the collimator and reconstruction parameters. The goal of this study is to determine how to perform this optimization, namely whether the collimator parameters can be optimized solely from projection data, or whether reconstruction parameters should also be considered. In order to answer this question, and to determine the optimal collimation, a digital phantom representing a human torso with 16 mm diameter hot lesions (activity ratio 8:1) was generated and used to simulate clinical SPECT studies with parallel-hole collimation. Two approaches to optimizing the SPECT system were then compared in a lesion quantification task: sequential optimization, where collimation was optimized on projection data using the Cramer–Rao bound, and joint optimization, which simultaneously optimized collimator and reconstruction parameters. For every condition, quantification performance in reconstructed images was evaluated using the root-mean-squared-error of 400 estimates of lesion activity. Compared to the joint-optimization approach, the sequential-optimization approach favoured a poorer resolution collimator, which, under some conditions, resulted in sub-optimal estimation performance. This implies that inclusion of the reconstruction parameters in the optimization procedure is important in obtaining the best possible task performance; in this study, this was achieved with a collimator resolution similar to that of a general-purpose (LEGP) collimator. This collimator was found to outperform the more commonly used high-resolution (LEHR) collimator, in agreement with other task-based studies, using both quantification and detection tasks.     

A Monte Carlo and physical phantom evaluation of quantitative In-111 SPECT

Accurate estimation of the 3D in vivo activity distribution is important for dose estimation in targeted radionuclide therapy (TRT). Although SPECT can potentially provide such estimates, SPECT without compensation for image degrading factors is not quantitatively accurate. In this work, we evaluated quantitative SPECT (QSPECT) reconstruction methods that include compensation for various physical effects. Experimental projection data were obtained using a GE VH/Hawkeye system and an RSD torso phantom. Known activities of In-111 chloride were placed in the lungs, liver, heart, background and two spherical compartments with inner diameters of 22 mm and 34 mm. The 3D NCAT phantom with organ activities based on clinically derived In-111 ibritumomab tiuxetan data was used for the Monte Carlo (MC) simulation studies. Low-noise projection data were simulated using previously validated MC simulation methods. Fifty sets of noisy projections with realistic count levels were generated. Reconstructions were performed using the OS-EM algorithm with various combinations of attenuation (A), scatter (S), geometric response (G), collimator-detector response (D) and partial volume compensation (PVC). The QSPECT images from the various combinations of compensations were evaluated in terms of the accuracy and precision of the estimates of the total activity in each organ. For experimental data, the errors in organ activities for ADS and PVC compensation were less than 6.5% except the smaller sphere (-11.9%). For the noisy simulated data, the errors in organ activity for ADS compensation were less than 5.5% except the lungs (20.9%) and blood vessels (15.2%). Errors for other combinations of compensations were significantly (A, AS) or somewhat (AGS) larger. With added PVC, the error in the organ activities improved slightly except for the lungs (11.5%) and blood vessels (3.6%) where the improvement was more substantial. The standard deviation/mean ratios were all less than 1.5%. We conclude that QSPECT methods with appropriate compensations provided accurate In-111 organ activity estimates. For the collimator used, AGS was almost as good as ADS and may be preferable due to the reduced reconstruction time. PVC was important for small structures such as tumours or for organs in close proximity to regions with high activity. The improved quantitative accuracy from QSPECT methods has the potential for improving organ dose estimations in TRT.     

OSEM重建算法中几个关键问题的研究

目的：改进平行孔准直器SPECT系统的成像方法，快速、精确地实现有序子集期望值最大化（OSEM）重建算法。方法：采用理想平行孔和张角效应平行孔准直器两种模型，将准直器的空间响应融入系统传输矩阵，利用改进的射线跟踪算法进行衰减校正。结果：随着准直器张角的增加，Jaszczak模型的重建图像在边界出现明显的亮环；利用考虑准直器空间响应的系统矩阵进行图像重建．能较好的抑制边界伪影。结论：融入准直器空间响应函数的系统矩阵更为精确、贴近真实情况，能较好的抑制边界伪影，提高了重建图像的对比度和信噪比。     

Implementation of an iterative scatter correction, the influence of attenuation map quality and their effect on absolute quantitation in SPECT

We investigated the accuracy of qSPECT, a quantitative SPECT reconstruction algorithm we have developed which employs corrections for collimator blurring, photon attenuation and scatter, and provides images in units of absolute radiotracer concentrations (kBq cm(-3)). Using simulated and experimental phantom data with characteristics similar to clinical cardiac perfusion data, we studied the implementation of a scatter correction (SC) as part of an iterative reconstruction protocol. Additionally, with experimental phantom studies we examined the influence of CT-based attenuation maps, relative to those obtained from conventional SPECT transmission scans, on SCs and quantitation. Our results indicate that the qSPECT estimated scatter corrections did not change appreciably after the third iteration of the reconstruction. For the simulated data, qSPECT concentrations agreed with images reconstructed using ideal, scatter-free, simulated data to within 6%. For the experimental data, we observed small systematic differences in the scatter fractions for data using different combinations of SCs and attenuation maps. The SCs were found to be significantly influenced by errors in image coregistration. The reconstructed concentrations using CT-based corrections were more quantitatively accurate than those using attenuation maps from conventional SPECT transmission scans. However, segmenting the attenuation maps from SPECT transmission scans could provide sufficient accuracy for most applications.     

Monte Carlo simulations of a scintillation camera using GATE: validation and application modelling

Geant4 application for tomographic emission (GATE) is a recently developed simulation platform based on Geant4, specifically designed for PET and SPECT studies. In this paper we present validation results of GATE based on the comparison of simulations against experimental data, acquired with a standard SPECT camera. The most important components of the scintillation camera were modelled. The photoelectric effect. Compton and Rayleigh scatter are included in the gamma transport process. Special attention was paid to the processes involved in the collimator: scatter, penetration and lead fluorescence. A LEHR and a MEGP collimator were modelled as closely as possible to their shape and dimensions. In the validation study, we compared the simulated and measured energy spectra of different isotopes: 99mTc, 22Na, 57Co and 67Ga. The sensitivity was evaluated by using sources at varying distances from the detector surface. Scatter component analysis was performed in different energy windows at different distances from the detector and for different attenuation geometries. Spatial resolution was evaluated using a 99mTc source at various distances. Overall results showed very good agreement between the acquisitions and the simulations. The clinical usefulness of GATE depends on its ability to use voxelized datasets. Therefore, a clinical extension was written so that digital patient data can be read in by the simulator as a source distribution or as an attenuating geometry. Following this validation we modelled two additional camera designs: the Beacon transmission device for attenuation correction and the Solstice scanner prototype with a rotating collimator. For the first setup a scatter analysis was performed and for the latter design. the simulated sensitivity results were compared against theoretical predictions. Both case studies demonstrated the flexibility and accuracy of GATE and exemplified its potential benefits in protocol optimization and in system design.     

System characteristics of SPECT with a slat collimated strip detector

In classical SPECT with parallel hole collimation, the sensitivity is constant over the field of view (FOV). This is no longer the case if a rotating slat collimator with planar photon collection is used: there will be a significant variation of the sensitivity within the FOV. Since not compensating for this inhomogeneous sensitivity distribution would result in non-quantitative images, an accurate knowledge of the sensitivity is mandatory to account for it during reconstruction. On the other hand, the spatial resolution versus distance dependency remains unaltered compared to parallel hole collimation. For deriving the sensitivity, different factors have to be taken into account: a first factor concerns the intrinsic detector properties and will be incorporated into the calculations as a detection efficiency term depending on the incident angle. The calculations are based on a second and more pronounced factor: the collimator and detector geometry. Several assumptions will be made for the calculation of the sensitivity formulae and it will be proven that these calculations deliver a valid prediction of the sensitivity at points far enough from the collimator. To derive a close field model which also accounts for points close to the collimator surface, a modified calculation method is used. After calculating the sensitivity in one plane it is easy to obtain the tomographic sensitivity. This is done by rotating the sensitivity maps for spin and camera rotation. The results derived from the calculations are then compared to simulation results and both show good agreement after including the aforementioned detection efficiency term. The validity of the calculations is also proven by measuring the sensitivity in the FOV of a prototype rotating slat gamma camera. An expression for the resolution of these planar collimation systems is obtained. It is shown that for equal collimator dimensions the same resolution-distance relationship is obtained as for parallel hole collimators. Although, a better spatial resolution can be obtained with our prototype camera due to the smaller pitch of the slats. This can be achieved without a major drop in system sensitivity due to the fact that the slats consist of less collimator material compared to a parallel hole collimator. The accuracy of the calculated resolution is proven by comparison with Monte Carlo simulation and measurement resolution values.     

Quantitative reconstruction for myocardial perfusion SPECT: an efficient approach by depth-dependent deconvolution and matrix rotation

An efficient reconstruction method for myocardial perfusion single-photon emission computed tomography (SPECT) has been developed which compensates simultaneously for attenuation, scatter, and resolution variation. The scattered photons in the primary-energy-window measurements are approximately removed by subtracting the weighted scatter-energy-window samples. The resolution variation is corrected by deconvolving the subtracted data with the detector-response kernel in frequency space using the depth-dependent frequency relation. The attenuated photons are compensated by recursively tracing the attenuation factors through the object-specific attenuation map. An experimental chest phantom with defects inside myocardium was used to test the method. The attenuation map of the phantom was reconstructed from transmission scans using a flat external source and a high-resolution parallel-hole collimator of a single-detector system. The detector-response kernel was approximated from measurements of a point source in air at several depths from the collimator surface. The emission data were acquired by the same detector setting. A computer simulation using similar protocols as in the experiment was performed. Both the simulation and experiment showed significant improvement in quantification with the proposed method, as compared to the conventional filtered-backprojection technique. The quantitative gain by the additional deconvolution was demonstrated. The computation time was less than 20 min on a HP/730 desktop computer for reconstruction of a 1282 x 64 array from 128 projections of 128 x 64 samples.     

A comparison of attenuation correction methods for quantitative single photon emission computed tomography

Transverse section tomograms of experimental phantoms and patients have been obtained using a GE 400T camera and a filtered back-projection reconstruction technique. These tomograms have been compared with the corresponding sections reconstructed from the same tomographic projection data, but using iterative algorithms with correction for photon attenuation. The comparison assesses the importance of including a correction for attenuation as well as demonstrating how closely a simple geometric attenuation correction, applied to the filtered back-projection reconstruction method, approximates to a more accurate correction incorporated in the computation of line integrals during iterative reconstruction. A comparison is also made between the behaviour of reconstruction algorithms with simulated projection data and real data in terms of convergence properties, and some shortcomings arising from simulation are noted.     

Simulation of HyperSPECT: a high-resolution small-animal system with in-line x-ray optics

SPECT has become an important tool in pre-clinical applications. Small-animal imaging systems based on the use of one or more pinhole collimators now reach sub-half-mm resolution but unfortunately suffer from a compromise between sensitivity and resolution due to the pinhole collimators. We propose a small-animal SPECT system based not on pinholes but on in-line x-ray optics, which is rare in medical imaging systems for nuclear medicine. The x-ray lenses are optimized for 27 keV for low-energy imaging with iodine-125. We believe that this new system, HyperSPECT, can simultaneously improve on sensitivity and resolution compared to today's state-of-the-art systems. A full three-dimensional simulation of the system has been performed including the prism-array lenses, pre- and post-collimators and scintillator-based detector. Images of capillary phantoms have been reconstructed using an iterative image reconstruction method. Sensitivity was uniformly 0.37% throughout the 1 cm diameter spherical field of view and rod sizes of around 100 μm diameter were distinguishable in the images of simulated capillary phantoms. These results indicate an increase in resolution by a factor of 5 during a simultaneous increase in sensitivity by a factor of 2 compared to the current state-of-the-art small-animal SPECT systems.     

Implementation of an accelerated iterative algorithm for cone-beam SPECT

In this paper we describe the implementation of an accelerated iterative reconstruction algorithm (AIRA) for cone-beam (CB) projections using a single circular orbit in single-photon-emission computed tomography (SPECT). This algorithm is a modified maximum-likelihood-expectation-maximization (ML-EM) algorithm and several approaches have been used to accelerate the reconstruction process. These approaches include: (i) the use of ordered subsets; (ii) the use of active areas and volumes; and (iii) the storing in memory of the transition vector for a given ray (during the forward projection step). This algorithm, which compensates for collimator geometric sensitivity variation as a function of position and makes uniform attenuation corrections has been evaluated using experimentally acquired phantom data. The results demonstrate a two-orders-of-magnitude decrease of the computational time of this algorithm over the conventional ML-EM algorithm with similar convergence properties.     

Cone beam collimation for single photon emission computed tomography: analysis, simulation, and image reconstruction using filtered backprojection

This paper presents an analysis of two cone beam configurations (having focal lengths of 40 and 60 cm) for the acquisition of single photon emission computed tomography (SPECT) projection data. A three-dimensional filtered backprojection algorithm is used to reconstruct SPECT images of cone beam projection data obtained using Monte Carlo simulations. The mathematical analysis resulted in on-axis point source sensitivities (calculated for a distance of 15 cm from the collimator surface) for cone beam configurations that were 1.4-3 times the sensitivities of parallel-hole and fan beam geometries having similar geometric resolutions. Cone beam collimation offers the potential for improved sensitivity for SPECT devices using large-field-of-view scintillation cameras.     

SNR Weighting for Shear Wave Speed Reconstruction in Tomoelastography

In tomoelastography, to achieve a final wave speed map by combining reconstructions obtained from all spatial directions and excitation frequencies, the use of weights is inevitable. Here, a new weighting scheme, which maximizes the signal‐to‐noise ratio (SNR) of the final wave speed map, has been proposed. To maximize the SNR of the final wave speed map, the use of squares of estimated SNR values of reconstructed individual maps has been proposed. Therefore, derivations of the SNR of the reconstructed wave speed maps have become necessary. Considering the noise on the complex MRI signal, the SNR of the reconstructed wave speed map was formulated by an analytical approach assuming a high SNR, and the results were verified using Monte Carlo simulations (MCSs). It has been assumed that the noise remains approximately Gaussian when the image SNR is high enough, despite the nonlinear operations in tomoelastography inversion. Hence, the SNR threshold was determined by comparing the SNR computed by MCSs and analytical approximations. The weighting scheme was evaluated for accuracy, spatial resolution and SNR performances on simulated phantoms. MR elastography (MRE) experiments on two different phantoms were conducted. Wave speed maps were generated for simulated 3D human abdomen MRE data and experimental human abdomen MRE data. The simulation results demonstrated that the SNR‐weighted inversion improved the SNR performance of the wave speed map by a factor of two compared to the performance of the original (i.e., amplitude‐weighted) reconstruction. In the case of a low SNR, no bias occurred in the wave speed map when SNR weighting was used, whereas 10% bias occurred when the original weighting (i.e., amplitude weighting) was used. Thus, while not altering the accuracy or spatial resolution of the wave speed map with the proposed weighting method, the SNR of the wave speed map has been significantly improved.